A sum of money was given to Arin, Greg, and James, the ratio is 2:5:7. James received $1180 more than Arin. How much total money was shared?

The quadratic is the left-most piece.  This exists on the interval (-infty, -2).

The linear piece is the center piece and exists on the interval (-2,6).

The square root piece is the right-most piece and exists on (6, infty).

These intervals are describing how each piece lines up with the x-axis, as illustrated in the picture.

The required description of the given piecewise function are as follows:

quadratic → (-∞, -2); linear → (-2, 6) and square root → (6, ∞).

A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).

The graph is given in the question, as shown

1. quadratic function:

This the sub-function define between the interval (-∞, -2).

2. linear function:

This the sub-function define between the interval (-2, 6).

3. square root function:

This the sub-function define between the interval (6, ∞).

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Using the fact that the angles are supplementary, we can write and solve a linear equation to find that x = 5°.

Remember that two angles are supplementary if the addition of their measures is equal to 180°.

Here we know that angles J and K are supplementary, then we know that:

J + K = 180°

Here we also know that:

J = 120°

K = 12x

So we can write a linear equation of the form:

120° + 12x = 180°

12x = 180° - 120°

12x = 60°

x = 60°/12 = 5°

x = 5°

We conclude that the value of x is 5°.

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Step-by-step explanation:

your teacher could have explained this better by telling us that A(t) is the remaining amount of the original isotope.

(a)

we start with 200 g and let it do its thing for 25 years.

all we need to do is enter the number of years into the function formula (as this is a college question you are able to work with functions, right ?) and calculate :

A(25) = 200e^(-0.054 × 25) = 200e^-1.35 =

= 51.84805213... g ≈ 51.85 g

after 25 years, about 51.85 g of the sample will be left.

assuming you have a calculator (at least on your computer) that was really "difficult", don't you think ?

(b)

half of the original amount is 200/2 = 100 g.

so, we need to find the value for t so that A(t) = 100.

100 = 200e^(-0.054 × t)

100/200 = 1/2 = 0.5 = e^(-0.054 × t)

ln(0.5) = -0.054 × t

t = ln(0.5) / -0.054 = 12.8360589... years

I assume you need to round to the nearest hundredth here as well :

after about 12.84 years the sample will decay to half of the original amount.

Answer:

I'll help

Step-by-step explanation:

the entrance fee to the skating rink=$5

each minute the skater uses the rink costs=$0.25

The solution to the inequality 6x > 72 is option B x > 12

What is an inequality?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

A is not equivalent to b in any scenario. Since a is strictly less than or strictly greater than b, these relationships are known as stringent inequalities. Equivalence is not considered.

There are two forms of inequality relations that are not strict, in contrast to strict inequalities:

The notation a ≤ b or a ⩽ b means that a is less than or equal to b (or, equivalently, at most b, or not greater than b).

The notation a ≥ b or a ⩾ b means that a is greater than or equal to b (or, equivalently, at least b, or not less than b).

Given, the inequality is 6x>72

6x > 72

Dividing by 6 on both sides of inequality, we get,

6x/6 > 72/6

⇒ x > 12

Hence, option B is correct.

The solution to the inequality 6x > 72 is option B, x > 12

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The term that makes NO distinction between an explanatory variable X and a response variable Y is Correlation , the correct option is (a) .

In the question ,

four options are given ,

we have to select the option that makes no distinction between explanatory variable X and a response variable Y .

Response Variable is the (dependent variable) measures the outcome of the study.

Explanatory Variable is the (independent variable) helps to explain or influence changes in a response variable.

So , Correlation makes no distinction between explanatory and response variables.

So , it makes no difference in calculating the correlation , which variable you call x and which you call y  .

Therefore , the correct option is (a) .

The given question is incomplete , the complete question is

Which of the following makes NO distinction between an explanatory variable X and a response variable Y (i.e., you can interchange the roles of X and Y and get the same result) ?

(a) Correlation

(b) Regression

(c) Both correlation and regression make no distinction between X and Y.

(d) Both correlation and regression make distinction between X and Y.

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Answer:

b) 2/9

c) 1/3

Step-by-step explanation:

The probability of a desired event happening is the number of ways the desired event can happen divided by the total number of possible outcomes.

a) Correct

b)

There are 9 possible outcomes.

2 outcomes are negative.

p(negative) = 2/9

c)

There are 3 outcomes that are more then 3.

p(more than 3) = 3/9 = 1/3

Answer:

x = 7

Step-by-step explanation:

x(XY) = 6(WX)

x(x + 11) = 6(6 + 15)

x² + 11x = 126

x² + 11x - 126 = 0

126 = 7 × 18

(x + 18)(x - 7) = 0

x + 18 = 0   or   x - 7 = 0

x = -18   or   x = 7

We discard the negative answer.

x = 7

Answer:

a=-2400

Step-by-step explanation:

We have -x*y*z = 150. We want to find the value of -2x*2y*-4z. Let's set this to a variable, a. We have now that [tex]2x*2y*4z = a[/tex] (because the negatives combine to a positive), where we want to solve for a. This is equal to [tex]16xyz = a[/tex], and dividing by 16 on both sides results in [tex]xyz = a/16[/tex]. Recall that we know [tex]-xyz = 150.[/tex] Negating each side gives us [tex]xyz = -150.[/tex]

Now we have two equations that are equal to the same thing(xyz), so we can set them equal to each other. This gives us [tex]-150 = a/16[/tex]. To solve for a, we multiply both sides by 16, giving us a = -2400. This is our answer!

Hope this helps!

Answer: Come up with questions that make sence. That are good solvablequestions. Make sure that you are able to take data off of it to see how people result in it.

Step-by-step explanation:

By using various properties of triangles, we get the value of [tex]\angle[/tex]ABD is 47.5°.

What are the properties of a triangle?

A triangle's sides and angles serve as the foundation for all of its characteristics. Triangular closed polygons with three sides and three vertices are what the word "triangle" means. The three internal angles of a triangle add up to 180°.

Let us first name a few angles that we will be using throughout the solution.

Let, [tex]\angle[/tex]DEN=a

[tex]\angle[/tex]ENC=c

[tex]\angle[/tex]MEB=b

[tex]\angle[/tex]EMB=d

Now, since it is given that AD ≅ AE, let us assume that triangle ADE is an isosceles triangle, with AD=AE.

Hence we get

[tex]\angle[/tex]DAE+[tex]\angle[/tex]ADE+[tex]\angle[/tex]AED=180° (angle sum property)

35°+2[tex]\angle[/tex]ADE=180°

[tex]\angle[/tex]ADE=[tex]\angle[/tex]AED=72.5°

Next, we know that

[tex]\angle[/tex]AED+a+[tex]\angle[/tex]NEC=180° (linear pair property of angles on a straight line)

72.5°+a+30°=180°

a=77.5°

Since a=b (opposite angles)
we get, a=b=77.5°

Now in triangle ENC, if we take the sum of angles, we get

[tex]\angle[/tex]NEC+[tex]\angle[/tex]NCE+c=180° (angle sum property)

30°+25°+c=180°

c=125°

We also know that the sum of interior angles made by an intersecting line between 2 parallel lines (given shape is a trapezoid) is 180, hence we get

c+d=180°

d=55°

In triangle MBN, we have

d+b+[tex]\angle[/tex]MBD=180° (angle sum property)

55°+77.5°+[tex]\angle[/tex]MBD=180°

[tex]\angle[/tex]MBD=47.5°

Therefore, we get the value of [tex]\angle[/tex]ABD=47.5°

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Answer:

x ≤ 10

Step-by-step explanation:

3/2 x - 1 ≤ x +4

3/2 x - x ≤ 1 + 4

(3-2)/2 x ≤ 5

1/2 x ≤ 5

2 * 1/2 x ≤  2 * 5

x ≤ 10

The probablity that the two balls are orange and blue is 1/8

Describe Probability:

This is the chance or likelihood that an event will take place.

One orange ball, one yellow ball, and two blue balls are there in a bag.

The total number of sample space  or outcome can be given as

Total outcome = 1 + 1 + 2=4

Probablity of occouring an orange ball  can be given as, 1/4

Probablity of occouring a blue ball  can be given as, 2/4

Probablity of an orange ball and a blue ball = 1/4 * 2/4

Probablity of an orange ball and a blue ball = 1/8

Consequently, there is a 1/8 chance that the two chosen balls are orange and blue

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The disparity -9x/11 - 7 < -5 is x > -22/9

The equals sign in the equation-like statement 5x 4 > 2x + 3 has been replaced by an arrowhead. This is a prime instance of inequality. This indicates that the left half, 5x 4, is larger than the right part, 2x + 3, in the equation.

Mathematical expressions with inequalities on both sides are known as inequalities. In an inequality, we compare two values as opposed to equations. In between, the equal sign is changed to a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The equals sign in the equation-like statement 5x 4 > 2x + 3 has been replaced by an arrowhead. This is a prime instance of inequality.

-9x/11 < 2 (add 7 to both sides) (add 7 to both sides)

-9x < 22 (multiply both sides by 11) (multiply both sides by 11)

x > 22/-9 Because you are dividing by a negative integer, change the sign.

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Answer: x > [tex]\frac{-22}{9}[/tex]

Step-by-step explanation:

     To solve this inequality, we will isolate the variable, x, with inverse operations.

   Given:

[tex]\frac{-9x}{11}[/tex]- 7 < -5

   Add 7 to both sides of the inequality:

[tex]\frac{-9x}{11}[/tex] < 2

   Multiply both sides of the inequality by 11:

-9x < 22

   Divide both sides of the inequality by -9:

* note, we must "flip" the sign since we are dividing by a negative integer

x > [tex]\frac{-22}{9}[/tex]

the total area of the two triangles as shwon in the image is 70 in²

Area can be defined as the total portion occuppied by a plane fiqure.

To calculate the total area of the two triangles, we use the formula below.

Formula:

Where:

Substitute these values into equation 1

Similarly,

Where:

Substitute these values into equation 2

Therefore, the total area of the two triangles is 40+30 = 70 in².

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Answer:

exponential

Step-by-step explanation:

the 14% of a number will be always greater because the numbers themselves will be greater

Different arrangements of the display are possible is 2520.

Given:

the artist r. locklen jones selects 5 paintings from a collection of 7 to display in a row.

Permutation :

A permutation is an arrangement of objects in a definite order. The members or elements of sets are arranged here in a sequence or linear order.

= [tex]7_P_5[/tex]

we know that,

[tex]n_P_r[/tex] = n! / ( n - r ) !

[tex]7_P_5[/tex] = 7! / ( 7 - 5 ) !

= 7! / ( 2 ) !

= 7! / 2!

= 7 * 6 * 5 * 4 * 3 * 2! / 2!

= 42 * 20 * 3

= 840 * 3

= 2520

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Answer:

Option C

The first two hours cost $4. Between two hours and six hours cost $2 per hour, and all hours after that cost $1.

Step-by-step explanation:

From the first part of the graph we can see that there is a flat rate of $4 for the first two hours. So the first two hours cost $4.

We can eliminate options A and B leaving C and D as only possible options.

Look at the second part of the graph

Between 2 hours and 6 hours(difference of 4 hours), the cost increases from $4 to $8 or an increase of $8

So rate per hour is $8/4 = $ 2 per hour between 2 hours and 6 hours

This information alone is enough to eliminate D but let's go to the rate beyond 6 hours just to make sure. This is the third part of the graph

Between 6 and 7 hours (1 hour) we can see the cost goes from $12 to $13 or a difference of $1. This means for every hour after 6 hours, the rate is $1 per hour.

So option C is the correct choice

The answer to this Question based on Linear Relation is given below

What is Linear Relation?

It is a relation between two variables in which one variable has linear behaviour as other

means if one variable increases or decreases then other variables does same behaviour linearly

Solution:

let us denote the battery by b and time by t

b = 54 - t/2

this relation satisfies all the conditions that are given in Question and gives variation of battery with time and this if plotted on graph will give a linear straight line

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To keep the obtuse isosceles triangle design, the railing that he should order a duplicate of to create his dining area is of:

12 meters.

A set of measurements can represent a triangle if the sum of the two smaller measurements is greater than the greater measures.

The measurements in this triangle are given as follows:

If he orders a duplicate of the largest measurement, the smallest measurement would be the base of the isosceles triangle, meaning that it would be an acute isosceles triangle.

Then he should order a duplicate of the smallest measurement, of 12 meters, as then they would be the sides between the obtuse angle of the isosceles triangle.

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Answer:

Step-by-step explanation:

To keep the obtuse isosceles triangle design, the railing that he should order a duplicate of to create his dining area is of:

12 meters.

When does a set of three measurements can represent a triangle?

A set of measurements can represent a triangle if the sum of the two smaller measurements is greater than the greater measures.

The measurements in this triangle are given as follows:

Smallest: 12 meters.

Largest: 22.8 meters.

If he orders a duplicate of the largest measurement, the smallest measurement would be the base of the isosceles triangle, meaning that it would be an acute isosceles triangle.

Then he should order a duplicate of the smallest measurement, of 12 meters, as then they would be the sides between the obtuse angle of the isosceles triangle.

a. The table for the given data is as follows :

Year                  2014       2015        2016       2017

Value (in $) 254000 293000 338000 372000

b. Domain and Range for the given relation is:

Domain : {2014, 2015, 2016, 2017}

Range : {254000, 293000, 338000, 372000}

c. From the table we observe that for each year it is having a unique value so it is related to the function.

What is Domain?

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x).

What is Range?

The range of a function is the set of values that the function assumes.

What is Relation?

A collection of ordered pairs having one item from each set makes up a relation between two sets. If the ordered pair (x,y) is present in the relation and the items x and y come from different sets, then the objects are said to be connected

a. The table for the given data is as follows :

Year                  2014       2015        2016       2017

Value (in $) 254000 293000 338000 372000

b. Domain and Range for the given relation is:

Domain : {2014, 2015, 2016, 2017}

Range : {254000, 293000, 338000, 372000}

c. From the table we observe that for each year it is having a unique value so it is related to the function.

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Answer:12

Step-by-step explanation:

The solution to the system substitution is (x , y) = (-3,3).

Here it is given that,

y=-2 x -3 and y= 3 x + 12

Take y=-2 x -3 as equation 1,

y= 3 x + 12  as equation 2'

by equating both equations,

-2x-3=3x+12

-3-12=3x+2x

5x=-15

x=-15/5

 =-3

substituting the value of x in the equation1

y=-2x-3

y=-2(-3)-3

 =3

Hence, The solution to the system substitution is (x , y) = (-3,3).

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The function [tex]y = (\frac{1}{2})^x[/tex] is a decreasing function.

The function [tex]y = (\frac{1}{2})^x[/tex] is shallower from left to right.

The value of the function [tex]y = (\frac{1}{2})^x[/tex] is unity at the y-intercept.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

The given function is [tex]y = (\frac{1}{2})^x[/tex] which is an exponential function cause the exponent is the variable.

Now, At x = - 2 y = 4 ⇒ (- 2, 4),

x = - 1, y = 2 ⇒ (- 1, 2).

x = 0, y = 1 ⇒ (0, 1).

x = 1, y = 1/2 ⇒ (1, 1/2).

x = 2, y = 1/4 ⇒ (2, 1/4).

x = 3, y = 1/8 ⇒ (3, 1/8).

The function is a decreasing function as the value of x increases the value of the function is decreasing.

The function is shallower from left to right.

The value of the function is unity at y-intercept as anything raised to the zero power is 1.

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Answer:

g(3) is 24

Step-by-step explanation:

To find the value of g(3), we need to plug 3 into the function g(x) and evaluate the resulting expression. The function g(x) is defined as g(x) = 3(2)^x. When we plug 3 into this function, we get g(3) = 3(2)^3. To evaluate this expression, we need to calculate 2^3, which is 8. Therefore, g(3) = 3 * 8 = 24.

In summary, the value of g(3) is 24.

Answer:

g(3) = 24

Step-by-step explanation:

Given information,

→ g(x) = 3(2)^x

Then the value of g(3) will be,

→ g(x) = 3(2)^x

→ g(3) = 3(2)³

→ g(3) = 3(8)

→ [ g(3) = 24 ]

Hence, the value of g(3) is 24.

A) The lead executives statement has been justified below considering the fall and rise of the graph line.

B) Between the years 7 and 8.

A) Looking at the attached graph, we can trace that the printed ad's revenue peaked at $3 million and then began to fall steadily. The online ad revenue started  with nothing and thereafter gradually increased in value to millions of dollars. Now, since the printed ad revenue has been declining and online ad revenue is seen to be increasing, it means that the lead executive's assertion is accurate.

B) Both curves are seen to intersect between the seventh and eighth year, I would say around the middle of year 7, and both online ads and printed ads generated an approximate revenue of $2.2 million each

Between the years 7 and 8.

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The system of linear inequalities is graphed is  x < -2; y ≤ -x+2. Hence option c is the correct.

What is inequality?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

The graph consists of two inequalities.

Since the one graph line is solid, thus the inequality sign either "less than or equal" or "greater than or equal". The other one is dotted, thus it will be less than or greater than

First find the equation of line.

One line passes through the points (-2,0) and (0,-2).

The equation of line that passes through the point (a,0) and (0,b) is

x/a + y/b = 1

The equation of the line is x/(-2) + y/(-2) =1

x + y = -2

y = -x - 2

The equation of the inequality will be either y ≤ -x - 2 or y ≥  -x - 2.

Putting x =0  and y = 0 in y ≤ -x - 2

0  ≤ - 0 -2

0≤ -2 (false)

In the graph (0,0) does not include in the shaded region. Therefore the inequality is   y ≤ -x - 2.

The second line is parallel to y-axis.

The equation of line will be x = a

The line passes through the point (-2,0)

Putting x = -2 and y =0  in x = a

-2 = a

Therefore the equation of the dotted line will be x = -2

The equation of the inequality will be either x > -2 and  x < -2:

Putting x =0  and y = 0 in x < -2

0 < -2

0 < -2 (false)

In the graph (0,0) does not include in the shaded region. Therefore the inequality is  x < -2.

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(a) The population of the state was 18.5 million in 2000. (b)The population of the state will reach 26.6 million in the year 2002

A population is a distinct collection of people, whether that group consists of a nation or a population that shares a specific trait.  A population is the group of people from which a statistical sample is taken in statistics. As a result, a population can be defined as any group of people who have something in common.

Since t = 0 ,

Then A = 18.5

(b) The population of the state will reach 26.6 million in the year 2002

2002, by using the formula is 18.5e^0.173*t

Given,

A= 26.6

Then,    

[tex]A = 18.5 x e^{(0.1708t)} 26.6[/tex]

  [tex]= 18.5 x e^{(0.1708t)} \frac{26.6}{18.5}[/tex]

  = [tex]e^{(0.1708t)} 1.437838[/tex]

   = [tex]e^{(0.1708t)} \ln (\frac{1.437838}{0.1708})[/tex]

t = 2.126116

t =2

Therefore, 2 is the round down to the nearest years. So 2002 is the approximate year the population reached 26.6 million.

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